相关论文: Tropical Hopf manifolds and contracting germs
We classify holomorphic Pfaff systems (possibly non locally decomposable) on certain Hopf manifolds. As consequence, we prove some integrability results. We also prove that any holomorphic distribution on a general (non-resonance) Hopf…
We compute the mod-2 cohomology of the collection of all symmetric groups as a Hopf ring, where the second product is the transfer product of Strickland and Turner. We first give examples of related Hopf rings from invariant theory and…
We classify in terms of Hopf-type properties mapping tori of residually finite Poincar\'e Duality groups with non-zero Euler characteristic. This generalises and gives a new proof of the analogous classification for fibered 3-manifolds.…
We say that a Hopf algebra H is semicocommutative if the right adjoint coaction factorizes through the tensor product of H with the center of H. For instance the commutative and the cocommutative Hopf algebras are semicocommutative. The…
We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.
We express the reduction types of Picard curves in terms of tropical invariants associated to binary quintics. We also give a general framework for tropical invariants associated to group actions on arbitrary varieties. The problem of…
A foliation on a compact manifold is uniform if each pair of leaves of the induced foliation on the universal cover are at finite Hausdorff distance from each other. We study uniform foliations with Reeb components. We give examples of such…
Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and…
We use piecewise polynomials to define tropical cocycles generalising the well-known notion of tropical Cartier divisors to higher codimensions. Groups of cocycles are tropical analogues of Chow cohomology groups. We also introduce an…
The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an…
The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There…
We introduce adic tropicalizations for subschemes of toric varieties as limits of Gubler models associated to polyhedral covers of the ordinary tropicalization. Our main result shows that Huber's adic analytification of a subscheme of a…
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is…
The abelian category of tetramodules over an associative bialgebra $A$ is related with the Gerstenhaber-Schack (GS) cohomology as $Ext_\Tetra(A,A)=H_\GS(A)$. We construct a 2-fold monoidal structure on the category of tetramodules of a…
The moduli space of graphs $M_{g,n}^{\mathrm{trop}}$ is a polyhedral object that mimics the behavior of the moduli spaces $M_{g,n}$, $\overline{M}_{g,n}$ of (stable) Riemann surfaces; this relationship has been made precise in several…
In this paper we study variations of the Hopf theorem concerning continuous maps $f$ of a compact Riemannian manifold $M$ of dimension $n$ to $\mathbb{R}^n$. We investigate the case when $M$ is a closed convex $n$-dimensional surface and…
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…
We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the…
We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf…
Let $G$ be a split semisimple algebraic group over a field and let $A^*$ be an oriented cohomology theory in the sense of Levine--Morel. We provide a uniform approach to the $A^*$-motives of geometrically cellular smooth projective…